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This article studies the constrained optimization problem of integrator chain multiagent systems from the distributed perspective. Particularly, all the agents collaborate to find an optimal solution of a global objective function summed by multiple local ones, each of which is just convex and belongs to an individual agent. However, the potential optimal solutions are simultaneously subject to set constraints and two kinds of equality constraints, i.e., individual equality constraint and aggregate equality constraint, whereas their involved constraint parameters are privately available to individual agents. With a proper coordinate transformation, a distributed optimization protocol is synthesized by introducing proper internal dynamics. Under the Lyapunov framework, it is shown with a convex theory that the synthesized distributed protocol enables the multiagent system to achieve the concerned constrained optimization objective. An example is finally given to confirm the optimization effectiveness.

The optimization problem of second-order discrete-time multiagent systems with set constraints is studied in this article. In particular, the involved agents cooperatively search an optimal solution of a global objective function summed by multiple local ones within the intersection of multiple constrained sets. We also consider that each pair of local objective function and constrained set is exclusively accessible to the respective agent, and each agent just interacts with its local neighbors. By borrowing from the consensus idea, a projection-based distributed optimization algorithm resorting to an auxiliary dynamics is first proposed without interacting the gradient information of local objective functions. Next, by considering the local objective functions being strongly convex, selection criteria of step size and algorithm parameter are built such that the unique solution to the concerned optimization problem is obtained. Moreover, by fixing a unit step size, it is also shown that the optimization result can be relaxed to the case with just convex local objective functions given a properly chosen algorithm parameter. Finally, practical and numerical examples are taken to verify the proposed optimization results.

This article studies a distributed constrained optimization problem of multiple agents characterized by Euler–Lagrange systems with unknown inertial parameters. The optimization objective is to compute a feasible solution within the intersection of a series of constrained sets such that a global payoff function summed by a group of local ones is minimized. Meanwhile, each local payoff function and constrained set are just privately available to their respective agent. To accomplish the concerned constrained optimization objective, a fully distributed continuous-time algorithm resorting to a projection-based auxiliary dynamics is synthesized without using global topology information. The proposed distributed optimization algorithm is privacy-preserving in the sense that no actual state information is exchanged between distinct agents during the seeking progress. Besides, the associated stability analysis is carried out in terms of the Lyapunov theorem. Finally, a source localization example is performed to verify the effectiveness of the proposed distributed optimization algorithm.